What is x^2-4x-y^2+10y+5=0 ?

The solution to x^2-4x-y^2+10y+5=0 is Hyperbola with (h,k)=(2,5),a=sqrt(26),b=sqrt(26)

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x^2-4x-y^2+10y+5=0

x^{2} - 4 x - y^{2} + 10 y + 5 = 0

(h, k) = (2, 5), a = 26, b = 26

Solution steps

x^{2} - 4 x - y^{2} + 10 y + 5 = 0

Rewrite

x^{2} - 4 x - y^{2} + 10 y + 5 = 0

in the form of a standard hyperbola equation

\frac{( y - 5 ) ^{2}}{( 26 ) ^{2}} - \frac{( x - 2 ) ^{2}}{( 26 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (2, 5), a = 26, b = 26

\frac{( y + 2 ) ^{2}}{2} - \frac{( x + 1 ) ^{2}}{2} = 1

(x - 3)^{2} - (y - 2)^{2} = 3

3 x^{2} - 5 y^{2} = 18

x^{2} - y^{2} - 6 x - 8 y + 9 = 0

x^{2} - 3 x + 2 y - y^{2} = 1

What is x^2-4x-y^2+10y+5=0 ?
The solution to x^2-4x-y^2+10y+5=0 is Hyperbola with (h,k)=(2,5),a=sqrt(26),b=sqrt(26)